Freeze to Death
Hypothermia, or freezing to death, isn't quite as exotic as being executed by an elephant. But it certainly belongs on this list, as it combines a slow struggle with a painful death.
The body freezes in gradual stages. While we start out at a normal 98 or so degrees F (37 degrees C), as the body cools we start shivering. That's a sign your muscles are beginning to realize that we need to generate heat, stat. When no heat is supplied, our muscles become stiff and wooden, which means our motor control and coordination go out the window. Note that if you're tumbling around making contact with the ground, you're probably getting colder. Your brain is also suffering; you can't think clearly or hold a thought.
And then the shivering stops.
Which is very, very bad. Because now your body isn't even creating a cursory heat, and your overall temperature plunges. Your body's organs and responses are so slowed that it might actually appear that you're dead before you even are. Luckily, you do lose consciousness at some point, so you've got that going for you. Still, an unpleasant and typically drawn-out way to go.